In classical algebraic geometry the polynomial ring (and it's various quotients) form the local building blocks of most of the objects of study. Phrased geometrically, the prime spectrum of the polynomial ring of \(n\)  variables is affine space \(^n\)  which covers or contains many of the spaces of interest. Like schemes which are locally prime spectra of rings, perfectoid spaces are build from perfectoid algebras using the adic spectrum functor of Huber (see [1]},[2]}, and [3]}). The perfectoid Tate algebra plays the role of the polynomial ring, and the perfectoid unit disk (defined below) plays the role of affine space.

The perfectoid unit disk is the adic space associated to the perfectoid Tate algebra:
\(^{n,} = \left(T_n^{},(T_n^{})^\circ \right).\) 
